parameter A. Suppose the probability of having a zero breakdown in a random chosen week is 0.2. (a) Find the value of ). [3 marb (b) Find the expectation and variance of the number of breakdowns in a week. 2 marb

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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1. The number of breakdowns per week follows a Poisson distribution with the mean
parameter A. Suppose the probability of having a zero breakdown in a randomly
chosen week is 0.2.
(a) Find the value of A.
[3 marks]
(b) Find the expectation and variance of the number of breakdowns in a week.
[2 marks]
(c) It is known that the machine has broken down in a randomly chosen week. What
is the probability that there is at most one breakdown?
[10 marks]
Transcribed Image Text:1. The number of breakdowns per week follows a Poisson distribution with the mean parameter A. Suppose the probability of having a zero breakdown in a randomly chosen week is 0.2. (a) Find the value of A. [3 marks] (b) Find the expectation and variance of the number of breakdowns in a week. [2 marks] (c) It is known that the machine has broken down in a randomly chosen week. What is the probability that there is at most one breakdown? [10 marks]
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